How does Skippy evolve into Glacie?

The sex check is the whole gate here, and it is worth doing before you sink anything into the Aniimo. A male Skippy will not take this path no matter how much you level it, so if the one you caught is male, the fix is catching another rather than grinding the one you have. Check first, then commit.

Past that, this is a normal evolution and it costs you materials. Evolving an Aniimo needs specific resources, and Alpha Aniimo are where evolution stones and similar drops come from. If you are holding a material and do not know where more of it comes from, open it in the menu: the entry tells you which Aniimo drop it and where to go for them. That saves you hunting blind.

Getting there without evolving anything

Catching an Alpha boss hands you the evolved form directly, with no evolution step and no materials spent. It is a different route to the same creature, and whether it is the better one depends on how comfortable you are with the Alpha fight versus how much of the material grind you have already done.

Evolution gating in this game goes wider than a level number. Some paths open by defeating Alpha bosses, some come out of the Pathfinder character talent tree, and certain side quests unlock alternate forms and secret evolutions. The linked guide on special and branching evolutions covers how all of that works.

Not settled: The evolved form's name is not settled across pre-launch builds. It shows up as Glacie, and also as Glaci and Glacy.